Lecture 24 8 251 Spring 2007 Lecture 24 Topics Dp brane Parallel Dp s X X X I X I 1 1 X I X I 2 2 2p 2 nI exp in 1 2 n Z 1 2p p 1 I I 0 0 n nI a 2 n 1 Dp brane x0 x1 xp Coordinates on brane x x xi i 1 2 3 p p 1 2 values N N coordinates xp 1 xd Normal to brane xa a p 1 d d p values DD coordinates 1 3 Lecture 24 8 251 Spring 2007 Thus Equation 1 becomes 1 1 x i xi 2 x a xa 2 2 2p Equation 2 holds Equation 3 1 2p p 1 I I I n n a 2 0 0 n 1 X a a X a 0 X a X a scalar 1 a X a X 2 a e in sin n n n n 0 X a X a 2 na e in n 0 a m nb m m n 0 ab 2p p 1 i i i i a a p p n n n n 1 n 1 M2 1 1 N N Nlongitudinal Ntransverse i Nl n 1 n ni a Nt n 1 n na Ground state M 2 1 State p pi tachyons gives rise to p pi pa 0 2 Lecture 24 8 251 Spring 2007 Where do these elds live Reasonable to say on the brane Right number of coordinates p 1 dim space But where did the xa go i i Next state 1 p p M 2 0 p 1 2 of these states What are they Photon states a i Also 1 p p lives on brane but has xa index Nothing to do with spacetime Inert scalar states d p massless scalars Physical interpretation Represent possible excitations casting 0 energy and 0 momentum displacing the brane See QFT theory of Goldstone Parallel Dp s Know everything about strings A and B New problem strings C and D note C D since orientation matters A 1 1 B 2 2 C 1 2 D 2 1 In general i j with 0 Di Dj Before always talking about same D branes so there was an implicity 1 1 always a X a X i 1 1 a a X 2 X 1 2 a e in sin n n n n 0 X a 2 na e in cos n n 0 3 Lecture 24 8 251 Spring 2007 1 2 0a X 2a X 1a Alternatively write as a 1 a a 0 X 2 X 1 2 0 2 1 i i i 1 a a p p 0 0 N 1 2 1 1 2 M N 1 0a 0a 2 2p p 1 N 1 Contribution of Quantum Oscillation 1 a a a a 2 2 0 0 T0 X2 X1 Contribution of Tension Length Now M 2 quantized but can for any sector choose sectors Ground states p pi 1 2 p pi 1 1 we know how to handle this one i i State 1 p p 1 2 D branes separate so now not massless photons a i State 1 p p 1 2 same mass Always a scalar state Suppose have 3 branes 4 Lecture 24 8 251 Spring 2007 String A i j String B j k Can interact to form one string between Di and Dk i j j k i k Then Dj doesn t notice the string anymore Theory of interacting gauge elds Dp brane parallel to Dq Coordinates have split into common D common N and split N D 5
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